Maurice Edu's stoppage-time goal sent Rangers into the last 16 of the Europa League after a thrilling Lisbon finish.
Rangers took the lead after 20 minutes through El Hadji Diouf's precise header from a Steven Davis cross.
Sporting levelled three minutes from the break when Rangers failed to clear a cross into the box and Pedro Mendes curled it in against his former club.
Yannick Djalo was left unmarked to head in after 82 minutes, but Edu stabbed home to ensure an away-goals victory.
Knocking out the club Rangers defeated on their way to the 2008 Uefa Cup final sets up a tie against PSV Eindhoven, the Dutch league leaders having overcome French outfit Lille 5-3 on aggregate after a 3-1 win in the Netherlands.
Rangers had reverted to their European formation of three central defenders, with captain David Weir at its heart after overcoming illness and Richard Foster at right-back.
John Fleck was a surprise choice on the left of midfield, with the versatile Steven Whittaker in an unusual central midfield role and Davis on the right.
Matias Fernandez, who scored in the first leg as a substitute for Sporting, started in midfield ahead of the man he replaced in the first leg, Maniche, while Marco Torsiglieri was in for the suspended Daniel Carrico in central defence.
Edu (centre) scored Rangers' late goal against Sporting
Under-pressure Sporting coach Paulo Sergio showed his attacking intent by starting midfielder Cristiano Oliveira instead of full-back Abel.
And Rangers were soon under pressure as they displayed their recent inability to hold on to possession.
Indeed, Whittaker was robbed by Djalo 25 yards from his own goal and the Sporting midfielder's low drive was beaten away for a corner by goalkeeper Allan McGregor.
Sporting took encouragement from Rangers' uncertainty and won a series of corners, but the Scots survived without too many nervous moments.
Walter Smith's side worked their way into the game and began to probe for openings up front, where Diouf had been preferred to Kyle Lafferty after the Northern Irishman profligacy in Glasgow.
And, when Foster prodded the ball forward for Davis, the midfielder's cross to the back post found the Senegal forward peeling off his marker and he headed back across goalkeeper Rui Patricio and into the waiting net.
Rangers were looking increasingly comfortable. However, just as it looked like the visitors would survive until half-time, a mix-up in defence led to the equaliser.
Weir failed to deal with a cross ball, it deflected off the startled Bartley and, when Helder Postiga played it back to Mendes at the edge of the box, the Portugal midfielder curled beautifully into the corner.
Diouf was involved in a head-to-head argument with Sporting defender Evaldo as the half-time whistle blew, the players being separated by the fourth official and Rangers coach Kenny McDowall.
It was the Lisbon side's turn to look fired up as the second half began and McGregor had to rise smartly to palm clear a curling Fernandez cross that would have crept in at the back post had the goalkeeper not conceded the first of three corners within eight minutes.
Sporting should have taken the lead when a chipped pass from Fernandez found Joao Pereira sneaking in behind the Rangers defence, but he headed over from eight yards.
The game was now flowing from end to end and, when a Davis header was saved by Rui Patricio, Sporting broke clear and McGregor had to block a low Pereira drive clear with his legs.
Rangers boss Smith made a surprise change after 71 minutes, withdrawing Weir, with Vladimir Weiss and Kyle Lafferty coming on for the veteran defender and the largely anonymous Fleck.
The visitors had adopted a more adventurous formation. However, when Sasa Papac was dispossessed on the touchline, Pereira's cross found Djalo at the back post and he headed powerfully past McGregor from 10 yards.
It looked like Sporting's run of six games without a victory was coming to an end until Foster played in David Healy and the substitute's ball across the face of goal was touched in by Edu from close range.
Live text and stats
Thursday, 24 February 2011
(HT 1-1)(agg 3-3)Rangers win on away goals rule
01 Rui Patricio
04 Anderson Polga
47 Joao Pereira
06 Mendes (Carlos Saleiro 81)
14 Fernandez (Coelho 90+1)
21 Alberto Zapater yellow card
23 Postiga (Andre Santos 86)
26 Andre Santos,
33 Diogo Solomao,
09 Carlos Saleiro
03 Weir (Lafferty 71)
07 Edu yellow card
10 Fleck (Weiss 71)
17 Diouf (Healy 82)
Ref: TagliaventoAtt: 15,375
Attempts on target
Attempts off target
90:00+5:04 The referee blows his whistle to end the game.
90:00+1:47 Assist on the goal came from David Healy.
90:00+1:47 GOAL - Maurice Edu:Sporting 2 - 2 Rangers Maurice Edu scores a goal from close range to the bottom left corner of the goal. Sporting 2 (3)-(3) 2 Rangers.
90:00+1:43 The ball is swung over by David Healy,
90:00+0:14 Pedro Rui Patricio restarts play with the free kick.
90:00+0:14 Substitution (Sporting) makes a substitution, with Nuno Andre Coelho coming on for Matias Fernandez.
90:00+0:14 Unfair challenge on Marco Torsiglieri by Kyle Bartley results in a free kick.
89:05 The ball is swung over by Vladimir Weiss.
88:10 Shot by Miguel Carlos Saleiro from deep inside the penalty area misses to the right of the target.
87:02 The ball is sent over by Yanick Djalo.
85:56 Substitution Filipe Andre Santos is brought on as a substitute for Helder Postiga.
82:25 Pedro Joao Pereira provided the assist for the goal.
82:25 GOAL - Yanick Djalo:Sporting 2 - 1 Rangers Yanick Djalo scores a headed goal from close range. Sporting 2 (3)-(2) 1 Rangers.
81:28 Substitution David Healy joins the action as a substitute, replacing El-Hadji Diouf.
80:14 Substitution Miguel Carlos Saleiro replaces Pedro Mendes.
80:04 Richard Foster has an effort at goal from outside the box which goes wide right of the goal.
79:46 Inswinging corner taken by El-Hadji Diouf from the left by-line.
79:32 El-Hadji Diouf sends in a cross, blocked by Pedro Joao Pereira.
77:43 A cross is delivered by Pedro Mendes.
75:54 Maurice Edu concedes a free kick for a foul on Pedro Joao Pereira. Direct free kick taken by Fernando Abel.
75:22 Vladimir Weiss delivers the ball, Correa Anderson Polga manages to make a clearance.
75:12 El-Hadji Diouf takes a short corner.
72:55 Marco Torsiglieri fouled by Kyle Lafferty, the ref awards a free kick. Free kick taken by Pedro Mendes.
71:44 Vladimir Weiss gives away a free kick for an unfair challenge on Fernando Abel. Matias Fernandez crosses the ball from the
free kick right-footed from right wing, clearance made by Madjid Bougherra.
69:54 Direct free kick taken by Allan McGregor.
69:54 Substitution Vladimir Weiss is brought on as a substitute for John Fleck.
69:54 Substitution Kyle Lafferty on for David Weir.
69:54 Helder Postiga challenges Madjid Bougherra unfairly and gives away a free kick.
69:47 Alberto Zapater crosses the ball, Sasa Papac manages to make a clearance.
68:48 Inswinging corner taken right-footed by Matias Fernandez from the left by-line.
66:16 Foul by Pedro Mendes on Steven Whittaker, free kick awarded. Strike comes in from Steven Whittaker from the free kick.
65:06 Madjid Bougherra is ruled offside. Pedro Rui Patricio restarts play with the free kick.
64:22 Inswinging corner taken left-footed by Steven Davis from the right by-line.
63:29 Effort on goal by Pedro Mendes from just inside the area clears the crossbar.
63:06 Pedro Joao Pereira takes a shot. Save by Allan McGregor.
62:47 The ball is sent over by El-Hadji Diouf, Steven Davis takes a shot. Save by Pedro Rui Patricio.
60:58 John Fleck produces a cross.
60:27 The ball is sent over by Yanick Djalo.
58:01 Free kick taken by Pedro Joao Pereira.
58:01 Booking Maurice Edu goes into the book.
57:56 Foul by Maurice Edu on Fernando Abel, free kick awarded.
55:47 The ball is swung over by Pedro Mendes, Pedro Joao Pereira has a headed effort from close range and clears the bar.
54:03 El-Hadji Diouf is caught offside. Pedro Rui Patricio takes the indirect free kick.
53:11 Outswinging corner taken right-footed by Matias Fernandez, clearance by Maurice Edu.
52:55 Fernando Abel takes a shot. Blocked by David Weir.
52:13 The ball is delivered by Fernando Abel, clearance by Madjid Bougherra.
50:58 Helder Postiga is ruled offside. Sasa Papac takes the free kick.
49:38 Outswinging corner taken by Matias Fernandez.
48:41 Foul by Madjid Bougherra on Helder Postiga, free kick awarded. Direct strike on goal from the free kick comes in from Matias
Fernandez, Allan McGregor makes a save.
48:13 Santos Evaldo delivers the ball, Madjid Bougherra makes a clearance.
46:40 Outswinging corner taken right-footed by Matias Fernandez from the right by-line, Header from deep inside the penalty area
by Marco Torsiglieri goes harmlessly over the crossbar.
45:01 The referee gets the second half underway.
45:00+0:08 The first half comes to an end.
41:26 GOAL - Pedro Mendes:Sporting 1 - 1 Rangers Pedro Mendes grabs a goal from just outside the penalty area to the bottom right corner of the goal. Sporting 1 (2)-(2) 1
41:04 Maurice Edu concedes a free kick for a foul on Marco Torsiglieri. Direct free kick taken by Alberto Zapater.
40:34 The referee blows for offside. Indirect free kick taken by Pedro Mendes.
37:06 The ball is delivered by Santos Evaldo.
36:47 The referee blows for offside. Correa Anderson Polga restarts play with the free kick.
36:18 The assistant referee signals for offside against Helder Postiga. Indirect free kick taken by Allan McGregor.
35:14 The ball is sent over by Yanick Djalo.
34:22 Shot from deep inside the area by Alberto Zapater goes over the bar.
30:37 Right-footed shot by Pedro Mendes went wide left of the net.
29:39 Pedro Joao Pereira produces a cross, Steven Whittaker manages to make a clearance.
28:35 Free kick awarded for a foul by Kyle Bartley on Pedro Joao Pereira. Fernando Abel delivers the ball from the free kick right-footed
from right wing.
28:12 Free kick awarded for an unfair challenge on Correa Anderson Polga by El-Hadji Diouf. Correa Anderson Polga takes the free
27:21 The assistant referee signals for offside against Steven Davis. Pedro Rui Patricio takes the free kick.
23:24 Matias Fernandez takes the outswinging corner, clearance by Steven Whittaker.
22:12 Yanick Djalo is ruled offside. Allan McGregor takes the free kick.
21:32 The ball is delivered by El-Hadji Diouf, Correa Anderson Polga manages to make a clearance.
20:36 Effort by Helder Postiga from a long way out goes over the crossbar.
19:17 Assist on the goal came from Steven Davis.
19:17 GOAL - El-Hadji Diouf:Sporting 0 - 1 Rangers El-Hadji Diouf scores a headed goal from close in. Sporting 0 (1)-(2) 1 Rangers.
19:12 A cross is delivered by Steven Davis,
17:17 Free kick awarded for an unfair challenge on Matias Fernandez by Sasa Papac. Matias Fernandez restarts play with the free
14:01 John Fleck decides to take a short corner.
12:00 Effort from 35 yards by El-Hadji Diouf missed to the right of the goal.
9:49 Direct free kick taken by David Weir.
9:49 Booking Alberto Zapater is shown a yellow card.
Correction - 9:37 Foul by Alberto Zapater on Steven Whittaker, free kick awarded.
9:37 awarded for a foul by Alberto Zapater on Steven Whittaker.
5:05 Matias Fernandez decides to take the corner short.
4:28 Matias Fernandez takes a inswinging corner from the left by-line to the near post, clearance made by Sasa Papac.
4:14 Yanick Djalo takes a shot. Save by Allan McGregor.
3:31 El-Hadji Diouf fouled by Fernando Abel, the ref awards a free kick. Sasa Papac takes the direct free kick.
0:00 The game kicks-off.
Live text and data provided by The Press Association.
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